The Evolution of the Lyman-alpha Luminosity Function during Reionization

The time frame in which hydrogen reionization occurred is highly uncertain, but can be constrained by observations of Lyman-alpha (Ly α ) emission from distant sources. Neutral hydrogen in the intergalactic medium (IGM) attenuates Ly α photons emitted by galaxies. As reionization progressed the IGM opacity decreased, increasing Ly α visibility. The galaxy Ly α luminosity function (LF) is thus a useful tool to constrain the timeline of reionization. In this work, we model the Ly α LF as a function of redshift, z = 5–10, and average IGM neutral hydrogen fraction, x ¯ Hɪ . We combine the Ly α luminosity probability distribution obtained from inhomogeneous reionization simulations with a model for the UV LF to model the Ly α LF. As the neutral fraction increases, the average number density of Ly α emitting galaxies decreases, and are less luminous, though for x ¯ Hɪ ≲ 0.4 there is only a small decrease in the Ly α LF. We use our model to infer the IGM neutral fraction at z = 6.6, 7.0, and 7.3 from observed Ly α LFs. We conclude that there is a significant increase in the neutral fraction with increasing redshift: x ¯ Hɪ ( z = 6.6 ) = 0.08 − 0.05 + 0.08 , x ¯ Hɪ ( z = 7.0 ) = 0.28 ± 0.05 and x ¯ Hɪ ( z = 7.3 ) = 0.83 − 0.07 + 0.06 . We predict trends in the Ly α luminosity density and Schechter parameters as a function of redshift and the neutral fraction. We find that the Ly α luminosity density decreases as the universe becomes more neutral. Furthermore, as the neutral fraction increases, the faint-end slope of the Ly α LF steepens, and the characteristic Ly α luminosity shifts to lower values; hence, we conclude that the evolving shape of the Ly α LF—not just its integral—is an important tool to study reionization.